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Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Yang, Jin, Tan, Yuanshun and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2019) Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy. Communications in Nonlinear Science and Numerical Simulation, 73. pp. 363-378. ISSN 1007-5704 (Print), 1878-7274 (Online) (doi:https://doi.org/10.1016/j.cnsns.2019.02.025)

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Abstract

Periodical applications of immunotherapy and chemotherapy play significant roles in cancer treatment and studies have shown that the evolution of tumour cells is subject to random events. In order to capture the effects of such noise we developed a stochastic tumour-immune dynamical model with pulsed treatment to describe combinations of immunotherapy with chemotherapy. By using theorems of the impulsive stochastic dynamical equation, the tumour free solution and the global positive solution of the proposed system were investigated. We then show that the expectations of the solutions are bounded. Furthermore, threshold conditions for extinction, non-persistence in the mean, weak persistence and stochastic persistence of tumour cells are provided. The results reveal that comprehensive therapy or noise can dominate the evolution of tumours. Finally, biological implications are addressed and a conclusion is presented.

Item Type: Article
Uncontrolled Keywords: Stochastic tumour-immune model, Pulsed therapy, Extinction and persistence, Lyapunov function
Subjects: S Agriculture > S Agriculture (General)
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Natural Resources Institute
Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Last Modified: 20 Mar 2019 10:28
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/23103

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